Rudin Theorem 1.20 (b)

  • Thread starter Dschumanji
  • Start date
  • #1
153
1
I understand the proof except for the following:

Suppose that -m2 < nx < m1 for positive integers m1, m2, n, and real number x.

Then there is an integer m with -m2 ≤ m ≤ m1 such that m-1 ≤ nx < m.

It definitely sounds reasonable, but it seems like a big jump in logic.
 

Answers and Replies

  • #2
jgens
Gold Member
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50
Let m be the least integer that is strictly greater than nx. It is a triviality to verify that this integer has the desired properties.
 
  • #3
1
0
Simple proof

Hi there,
I have attached a simple demonstration of the bit you are asking.
Let me know if it is clear now.
I hope it helps
 

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